2. Let D be a distribution over R where the mean is 5 and variance is 9. Suppose x1, ... , x10 are indepen-dent draws from D. Plot the possible positions of these random variables on the real line.3. Let w E Rd be the variable, and let x E Rd and y E R be given. Calculate the gradient of the followingfunctions with respect to w:• F(w) = (y – w· x)100;• F(w) = vrwsi1y+w.x'• F(w) = log(1+ yw · x);F(w) = e(w-x)².

Python Programming Language has been used for the sample and plot generation. import numpy as…

2. Let D be a distribution over R where the mean is 5 and variance is 9. Suppose x1, . . . , x10 are indepen. dent draws from D. Plot the possible positions of these random variables on the real line.

2. Let D be a distribution over R where the mean is 5 and variance is 9. Suppose x1, . . . , x10 are indepen. dent draws from D. Plot the possible positions of these random variables on the real line.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter12: Review Of Calculus And Probability

Section12.5: Random Variables, Mean, Variance, And Covariance

Problem 3P

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Question

2. Let D be a distribution over R where the mean is 5 and variance is 9. Suppose x1, ... , x10 are indepen-
dent draws from D. Plot the possible positions of these random variables on the real line.
3. Let w E Rd be the variable, and let x E Rd and y E R be given. Calculate the gradient of the following
functions with respect to w:
• F(w) = (y – w
· x)100;
• F(w) = vrwsi
1
y+w.x'
• F(w) = log(1+ yw · x);
F(w) = e(w-x)².

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